Question

The sum of two numbers is 100 and the difference between their squares is 256000. find the number.

Answer 1

X + Y = 100. .....(1)
x^2 - Y^2 = 25600 .....(2)

Now,
X = 100 - Y equation (1) can be written like this
substitute (1) in the (2) equation.
so now,
(100 - Y)^2 - Y^2 = 25600
expand it using (a-b)^2 formula
(a-b)^2 = a^2 + b^2 - 2ab
10000 + Y^2 - 2(100)(Y) - Y^2 = 25600
10000 - 200Y = 25600
- 200Y = 25600 - 10000
- 200Y = 15600
Y = 15600 / (-200)
Y = -78
Now substitute Y value in equation (1)
X + Y = 100
X + (-78) = 100
X - 78 = 100
X = 178
therefore the values which satisfies the given conditions
1) X + Y = 100
2) X^2 - Y^2 = 25600 are X =178,Y = -78.